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Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2  and the largest odd number less than 3x+5 can be written in the form ax+b . What is a+b?

Guest Oct 8, 2017
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"Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2  and the largest odd number less than 3x+5 can be written in the form ax+b . What is a+b?"

 

If x is even then 7x - 2 is even, so the smallest odd number greater than 7x - 2 is 7x - 2 + 1 or 7x - 1

 

With x even then 3x + 5 is odd, so the largets odd number less than 3x + 5 is 3x + 5 - 2 or 3x + 3

 

Difference:  7x - 1 - (3x + 3) = 4x - 4  

 

ax + b = 4x - 4  so a = 4, b = -4

 

a + b = 0.

Alan  Oct 8, 2017

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